Emergence of Collective Organizational Phenomena in Manybody Systems

由微观力量控制的量子世界与主导我们日常生活的宏观世界之间的联系还没有被很好地理解。宏观系统表现出普遍的行为，不能敏感地依赖于微观细节，但被认为受制于强大的一般组织原则。宇宙行为在许多物理学分支的各种感兴趣的系统中都可以看到，包括早期宇宙的夸克-胶子等离子体，高温超导和实验室中的超冷费米气体。在这个项目中，P.I.将调查这些导致宏观系统集体行为的强大力量的出现。该计划是对作为系统大小函数的性质进行系统研究，重点放在被称为介观区域的中间区域，在那里量子力学和经典力学融合在一起。本科生和研究生都将全面参与这项研究，包括通过论文和演讲交流结果。这项研究的科学目标是阐明这种新兴的普遍行为背后的驱动力，并提出在实验室观察和控制这种行为的新方法。在过去的十年里，原子物理界利用冷却和捕获技术来创造和控制表现出普遍性质的有限大小的超冷气体系统。这项工作将集中于费米气体，并利用微扰方法，同时产生所有系统大小的精确一阶结果。通过研究作为系统大小函数的特性的趋势，例如最近在实验室测量的激发频率和热力学量，目标是揭示新出现的集体行为的特征，以便理解这一根本转变的动力学。

The connection between the quantum world controlled by microscopic forces and the macroscopic world that dominates our everyday lives is not well understood. Macroscopic systems exhibit universal behavior that cannot depend sensitively on microscopic details, but is believed to be subject to powerful and general principles of organization. Universal behavior is seen in a variety of systems of interest across many branches of physics including the quark-gluon plasma of the early universe, high temperature superconductivity and ultracold Fermi gases in the laboratory. In this project, the P.I. will investigate the emergence of these powerful forces that give rise to the collective behavior of macroscopic systems. The plan is to perform a systematic study of properties as a function of system size, focusing on an intermediate regime called the mesoscopic region where quantum mechanics and classical mechanics merge. Both undergraduate and graduate students will participate fully in this research, including communicating the results through papers and talks.The scientific goal of this study is to elucidate the driving forces behind this emerging universal behavior and to propose new ways to observe and control this behavior in the laboratory. In the last decade, the atomic physics community has taken advantage of cooling and trapping techniques to create and control finite-size systems of ultracold gases that exhibit universal properties. This work will focus on Fermi gases and utilize a perturbation method that yields exact first-order results for all system sizes simultaneously. By studying trends as a function of system size for properties such as excitation frequencies and thermodynamic quantities recently measured in the laboratory, the goal is to uncover signatures of emerging collective behavior in order to understand the dynamics of this fundamental transition.